Planetary Boundary Layer Model Research Articles

Quasi-Steady Analysis of a PBL Model with an Eddy-Diffusivity Profile and Nonlocal Fluxes

Analytic solutions to a planetary boundary layer (PBL) model with an eddy-diffusivity profile (i.e., a K profile) and nonlocal fluxes are presented for the quasi-steady regime. The solutions demonstrate how different processes contribute to the quasi-steady profiles of heat and/or other scalars in the convective boundary layer. It is shown that for a standard cubic form of the K profile, and flux scales based on the surface fluxes, the nondimensional nonlocal term should be less than six; larger values can cause scalar profiles of water vapor to increase with height in the upper portion of the PBL and can produce weakly superadiabatic layers in the upper PBL temperature profiles. Solutions are also shown to be sensitive to the choice of flux scale: fluxes scaled by their vertically averaged values imply that nondimensional profiles of top-down scalars will have a neutral point somewhere in the PBL, a result in conflict with previous work on the subject, and the predictions of the same model with fluxes scaled by their surface values. The analysis also shows that allowing K to go to zero with the square of the distance from the PBL top results in nonconvergent profiles; in general K should reduce to some positive value at the top of the PBL, or go to zero less rapidly. It is further shown that the class of models investigated here may be physically interpreted as relaxation models, that is, they tend to relax profiles of scalars in the PBL to implicitly defined similarity profiles on a convective timescale. Finally, analysis of a 1-yr integration of a climate model, interpreted in light of the author’s analytic results, suggests that a dynamically important aspect of the nonlocal term is its role in ventilating the surface layer, and thereby indirectly affecting the diagnoses of PBL depth in many models.

Application of a numerical model for the planetary boundary layer to the vertical distribution of radon and its daughter products

A one-dimensional numerical planetary boundary layer (PBL) model is developed and applied to study the vertical distribution of radon and its daughter products in the atmosphere. The meteorological model contains parameterization for the vertical diffusion coefficient based on turbulent kinetic energy and energy dissipation ( E– ε model). The increased vertical resolution and the realistic concentration of radon and its daughter products based on the time-dependent PBL model is compared with the steady-state model results and field observations. The ratio of radon concentration at higher levels to that at the surface has been studied to see the effects of atmospheric stability. The significant change in the vertical profile of concentration due to decoupling of the upper portion of the boundary layer from the shallow lower stable layer is explained by the PBL model. The disequilibrium ratio of 214 Bi/ 214 Pb broadly agrees with the observed field values. The sharp decrease in the ratio during transition from unstable to stable atmospheric condition is also reproduced by the model.

Evidence of a Mixed-Layer Dynamics Contribution to the Entrainment Process

The internal thermal boundary layer developing over the Mediterranean during a cold-air outbreak associated with a Tramontane event has been studied by means of airborne lidar, in situ sensors, and a modelling approach that consisted of nesting the University of Washington (UW) planetary boundary-layer (PBL) model in an advective zero-order jump model. This approach bypasses some of the deficiencies associated with each model: the absence of the dynamics in the mixed layer for the zero-order jump model and the lack of an inversion at the PBL top for the UW PBL model. Particular attention is given to the parameterization of the entrainment flux at the PBL top. Values of the entrainment closure parameter derived with the model when matching PBL structure observations are much lower than those derived with standard zero-order jump models. They also are in good agreement with values measured in different meteorological situations by other studies. This improvement is a result of the introduction of turbulent kinetic energy production in the mixed layer.

Comments on “A Multiscale Numerical Study of Hurricane Andrew (1992). Part I: Explicit Simulation and Verification”

AbstractNo abstract available. Corresponding author address: Dr. Mark D. Powell, NOAA-HRD-AOML, 4301 Rickenbacker Cswy., Miami, FL 33149. Email: powell@aoml.noaa.gov

Surface Winds at Landfall of Hurricane Andrew (1992)—A Reply

and ocean, separately, and then merging them along the coastline without including full dynamics and physics interaction,’’ as mentioned in LZY. In this reply, we will show that their converting the flight-level (at an altitude of 2.5‐3.2 km) data with a simple, one-dimensional planetary boundary layer (PBL) model tended to introduce large errors in surface winds, while their merging, without considering a transition zone produced by horizontal momentum advection, accounts for the unrealistic sharp discontinuity. These problems could be clear

Uncertainty in the Specification of Surface Characteristics, Part ii: Hierarchy of Interaction-Explicit Statistical Analysis

The uncertainty in the specification of surface characteristics in soil-vegetation- atmosphere-transfer (SVAT) schemes within planetary boundary-layer (PBL) or mesoscale models is addressed. The hypothesis to be tested is whether the errors in the specification of the individual parameters are accumulative or whether they tend to balance each other in the overall sense for the system. A hierarchy of statistical applications is developed: classical one-at-a-time (OAT) approach, level 1; linear analysis of variance (ANOVA), level 1.5; fractional factorial (FF), or level 2; two-factor interaction (TFI) technique, or level 2.5; and a non-linear response surface methodology (RSM), or level 3. Using the First ISLSCP Field Experiment (FIFE) observations for June 6, 1987 as the initial condition for a SVAT scheme dynamically coupled to a PBL model, the interactions between uncertainty errors are analyzed. A secondary objective addresses the temporal changes in the uncertainty pattern using data for morning, afternoon, and evening conditions. It is found that the outcome from the level 1 OAT-like studies can be considered as the limiting uncertainty values for the majority of mesoscale cases. From the higher-level analyses, it is concluded that for most of the moderate surface scenarios, the effective uncertainty from the individual parameters is balanced and thus lowered. However, for the extreme cases, such as near wilting or saturation soil moisture, the uncertainties add up synergistically and these effects can be even greater than those from the outcomes of the OAT-like studies. Thus, parameter uncertainty cannot be simply related to its deviation alone, but is also dependent on other parameter settings. Also, from the temporal changes in the interaction pattern studies, it is found that, for the morning case soil texture is the important parameter, for afternoon vegetation parameters are crucial, while for the evening case soil moisture is capable of propagating maximum uncertainty in the SVAT processes. Finally, a generic hypothesis is presented that an appropriate question for analysis has to be rephrased from the previous 'which parameters are significant?’ to 'what scenarios make a particular parameter significant?’

Numerical Models of Boundary Layer Processes over and around the Gulf of Mexico during a Return-Flow Event

Abstract The return-flow of low-level air from the Gulf of Mexico over the southeast United States during the cool season is studied using numerical models. The key models are a newly developed airmass transformation (AMT) model and a one-dimensional planetary boundary layer (PBL) model. Both are employed to examine the thermodynamic structure over and to the north of the Gulf. Model errors for predicting minimum, maximum, and dewpoint temperatures at the surface during both offshore and onshore phases of the return-flow cycle are analyzed. PBL model forecasts indicate soil moisture values obtained from the Eta Model improve accuracy. It is shown that forecasts of maximum temperature for coastal locations are sensitive to the soil moisture used in the PBL model. The AMT model performs well in determining boundary layer parameters since it includes horizontal advective processes. The AMT model is also able to predict the regional differences caused by different surface forcing while passing over land or se...

Numerical peculiarities in solving the planetary boundary layer equations

The numerical experiments performed with all possible combinations of approximations for the equations of a one-dimensional planetary boundary layer model employing a one-equation turbulence closure scheme and a staggered, homogenous, finite-difference grid show that numerical peculiarities in the form of spikes and jittering can be detected in the vertical profiles of the predicted variables. It is found that these peculiarities are caused by an inappropriate numerical description of the turbulent kinetic energy equation. Spikes occur for large time steps only and have a life time of several days. There exist two types of jittering: transient and permanent. The former has a lifetime of about 1 week and occurs with large time steps, whereas the latter has a lifetime of more than a 1000 days and is observed when using moderate time steps. It is found that transition to instability of the solution can either be a sudden or a gradual one. In the first case, no numerical peculiarities are observed, whereas in the second case, jittering is present during the entire transition period. In this sense, jittering may be regarded as a herald of instability. The only way of avoiding these numerical artefacts is to employ implicit approximations consistently for all the terms in the model equations.

Predicting Regional Transpiration at Elevated Atmospheric CO2: Influence of the PBL–Vegetation Interaction

Abstract A coupled planetary boundary layer (PBL)–vegetation model is used to study the influence of the PBL–vegetation interaction and the ambient CO2 concentration on surface resistance rs and regional transpiration λE. Vegetation is described using the big-leaf model in which rs is modeled by means of a coupled photosynthesis–resistance model. The PBL part is a one-dimensional, first-order closure model. Nonlocal turbulent transport is accounted for by means of a countergradient correction. The PBL model also describes CO2 fluxes and concentrations, which are driven by photosynthesis of the canopy. A number of sensitivity analyses are presented in which the behavior of rs and λE at an atmospheric CO2 concentration representative for the present-day situation is compared to their behavior under an approximately doubled CO2 concentration. The results reveal a positive atmospheric feedback on rs, by which an initial increase of rs, due to changes in ambient CO2 concentration, is magnified. The stomatal hu...

Feasibility of Retrieving Aerosol Concentration in the Atmospheric Boundary Layer Using Multitime Lidar Returns and Visual Range

Abstract This paper studies the feasibility of retrieving aerosol concentrations in the planetary boundary layer (PBL) with a variational data assimilation (VDA) algorithm using dual-wavelength lidar returns and visual range simulated at multiple times. Aerosols are assumed to consist of nucleation, accumulation, and coarse modes, with each mode distributed in a gamma distribution. The VDA algorithm retrieves initial vertical profiles of aerosol concentrations of the three modes, which are predicted by a 1D PBL model. The accuracy of retrieved aerosol concentrations of the three modes is examined through a series of identical twin numerical experiments. For the VDA algorithm that uses data from a lidar wavelength pair (0.289, 11.15 μm), results show that 1) if both random and systematic errors in the observed data are less than 1.0 dB and the number densities of accumulation and coarse modes are, respectively, 0.025–0.25 and 0–1.25 × 10−3 times that of the nucleation mode, relative errors in the retrieved...

Construction of Marine Surface Pressure Fields from Scatterometer Winds Alone

A series of 6-h, synoptic, gridded, global surface wind fields with a resolution of 100 km was generated using the dataset of dealiased Seasat satellite scatterometer (SASS) winds produced as described by Peteherych et al. This paper is an account of the construction of surface pressure fields from these SASS synoptic wind fields only, as carried out by different methods, and the comparison of these pressure fields with National Centers for Environmental Prediction (NCEP) analyses, with the pressure fields of the European Centre for Medium-Range Weather Forecasts (ECMWF), and with the special analyses of the Gulf of Alaska Experiment. One of the methods we use to derive the pressure fields utilizes a two-layer planetary boundary layer (PBL) model iterative scheme that relates the geostrophic wind vector to the surface wind vector, surface roughness, humidity, diabatic and baroclinic effects, and secondary flow. A second method involves the assumption of zero two-dimensional divergence, leading to a Poisson equation (the “balance equation”) in pressure, with the wind field serving as a forcing function. The pressure fields computed from the SASS winds using a two-layer PBL model closely approximate the NCEP and ECMWF fields. In some cases, the PBL-model-derived pressure fields can detect mesoscale features not resolved in either the NCEP or ECMWF analyses. Balanced pressure fields are much smoother and less well resolved than the PBL-model-derived or NCEP fields. Systematic differences between balanced pressure fields and the PBL-model-derived fields are attributed to the neglect of horizontal divergence in the balance equation. The effect of stratification is found to produce a larger impact than secondary flow or thermal wind effects on the derived pressure fields. Inclusion of secondary flow tends to weaken both low and high pressure centers, whereas inclusion of stratification intensifies low centers and weakens high centers.

Evaluation of sensitivity of land surface hydrology representations with and without land–atmosphere feedback

This paper compares various ways of quantifying the importance of land–atmosphere feedback. A widely used land surface hydrology model is used in coupled (to a planetary boundary layer model) and uncoupled modes to compare the adequacy of different feedback indices. It is found that existing feedback indices are primarily based on ‘one factor at a time’ sensitivity analysis and cannot adequately capture the interaction between land and atmosphere. A new index is used which combines factorial design concepts and traditional sensitivity analysis. This index is shown to capture and quantify the strength of interaction between land surface parameters and atmosphere. To assess the effects of forcing characteristics on the stand alone model sensitivity, several ways to specify near-surface atmospheric conditions are evaluated. It is found that commonly used forcing conditions (e.g. model generated or observed time-series of near-surface atmospheric variables) may not be adequate to mimic the coupled model environment for evaluating the land surface representations. The partially coupled model sensitivity is shown to capture a major feedback loop related to water holding capacity, surface fluxes and near-surface atmospheric processes. These results suggest that sensitivity from the stand alone model should be interpreted with caution and future evaluations should strive to incorporate land–atmosphere feedback, at least within a partially coupled model. © 1997 John Wiley & Sons, Ltd.

SPIKES AND JITTERING IN THE NUMERICAL SOLUTION OF THE PLANETARY BOUNDARY LAYER PROBLEM: CAUSES AND EFFECTS

Numerical experiments performed with all possible combinations of approximations for the equations of a one-dimensional planetary boundary layer model employing a one-equation turbulence closure scheme and a staggered, homogeneous, finite difference grid show that spikes and jittering in the vertical profiles of predicted variables are caused by an inappropriate numerical description of the turbulent kinetic energy equation. Jittering arises when using both moderate and large time steps, while spikes occur for large time steps only. There exist two types of jittering: transient and permanent. The former has a lifetime of about 1 week and occurs with large time steps. Permanent jittering, on the other hand, is observed when using moderate time steps and has a lifetime of more than a 1000 days. Introducing an iterative procedure for the eddy viscosity eliminates spikes and permanent jittering but is unsuccessful in removing transient jittering. It is further found that the transition to instability of the solution can be either a sudden or a gradual one. In the case of a sudden transition no numerical peculiarities are observed, whereas for a gradual transition to instability, jittering is present during the entire transition period. In this sense, jittering may be regarded as a herald of instability. Finally, a combination which employs implicit approximations consistently for all the terms in the model equations, regardless of whether using an implicit or semi-implicit approximation for the Coriolis term, proves to be devoid of any numerical artefacts without the need for introducing the iterative procedure for the eddy viscosity. © 1997 John Wiley & Sons, Ltd.

SPIKES AND JITTERING IN THE NUMERICAL SOLUTION OF THE PLANETARY BOUNDARY LAYER PROBLEM: CAUSES AND EFFECTS

Numerical experiments performed with all possible combinations of approximations for the equations of a one-dimensional planetary boundary layer model employing a one-equation turbulence closure scheme and a staggered, homogeneous, finite difference grid show that spikes and jittering in the vertical profiles of predicted variables are caused by an inappropriate numerical description of the turbulent kinetic energy equation. Jittering arises when using both moderate and large time steps, while spikes occur for large time steps only. There exist two types of jittering: transient and permanent. The former has a lifetime of about 1 week and occurs with large time steps. Permanent jittering, on the other hand, is observed when using moderate time steps and has a lifetime of more than a 1000 days. Introducing an iterative procedure for the eddy viscosity eliminates spikes and permanent jittering but is unsuccessful in removing transient jittering. It is further found that the transition to instability of the solution can be either a sudden or a gradual one. In the case of a sudden transition no numerical peculiarities are observed, whereas for a gradual transition to instability, jittering is present during the entire transition period. In this sense, jittering may be regarded as a herald of instability. Finally, a combination which employs implicit approximations consistently for all the terms in the model equations, regardless of whether using an implicit or semi-implicit approximation for the Coriolis term, proves to be devoid of any numerical artefacts without the need for introducing the iterative procedure for the eddy viscosity. © 1997 John Wiley & Sons, Ltd.

A dynamic statistical experiment for atmospheric interactions

Interactions among atmospheric parameters exist at different scales. The pristine approach for observational or model data analysis involves changing the input parameters one at a time (OAT) and studying the effect on the system. Limitations of this approach for atmospheric applications are discussed. A fractional factorial (FF) based study is evolved and a methodology is outlined involving dynamic graphical analysis. Observational data from the FIFE and HAPEX‐MOBILHY experiments are utilized with a vegetation and soil moisture scheme dynamically coupled in a planetary boundary layer model to demonstrate the robustness of this approach. Both low‐resolution and high‐resolution designs are considered. Various aspects of the vegetation‐atmosphere interactions are delineated. Results obtained from the interaction‐based FF approach differ considerably from the earlier OAT‐type studies.

Daytime variation of sensible heat flux estimated by the bulk aerodynamic method over a grass canopy

A study was performed to evaluate the bulk aerodynamic method for estimating daytime variation of sensible heat flux ( H A) for a wetted and non-wetted grass canopy under clear and cloudy days. The aerodynamic resistance applied was corrected for atmospheric stability using the Oregon State University One-Dimensional Planetary Boundary Layer model stability function. The performance of the bulk aerodynamic method was tested with indirect measurements of sensible heat flux ( H B) derived from the Bowen ratio energy balance method on 20-min time intervals. Results indicate that there was a good agreement between H B and H A with a coefficient of correlation of 0.93 and slope of the regression line through the origin of 0.96.

Wind and pressure fields near tropical cyclone Oliver derived from scatterometer observations

The results of this study demonstrate that the surface wind velocity and pressure fields derived from spaceborne scatterometers are useful in monitoring the location and intensity of tropical cyclones. Satellite‐borne microwave scatterometers can penetrate the cloudy core regions of tropical cyclones to resolve the circulation in detail over data sparse regions. The location of the cyclone observed by the ERS‐1 scatterometer is very close to that revealed in Geostationary Meteorological Satellite images. The surface winds provided by the ERS‐1 scatterometer are used here with a modified two‐layer planetary boundary layer model which includes effects of curvature, stability, and secondary flow to derive surface pressures near tropical cyclone Oliver. The curvature effect is found to be more significant than stability and secondary flow, which are crucial in deriving accurate surface pressure fields in midlatitudes.

A Study of Near-Surface Winds in Marine Cyclones Using Multiple Satellite Sensors

Abstract Synoptic-scale surface wind fields are developed using data from two Special Sensor Microwave/Imager (SSM/1) passive radiometers and the European Remote Sensing Satellite-1 (ERS-1) scatterometer for the lifetime of two northern Pacific winter storms. The data are merged with surface wind output from a planetary boundary layer (PBL) model. The inputs to the PBL model are from the European Centre for Medium-Range Weather Forecasts (ECMWF) global analyses. A method for interpolating these analyses to the time of the satellite passage, while preserving fundamental storm characteristics, was developed. Composite wind fields are constructed each time one or more of the satellites views the storms. These composite wind fields are compared to the near-surface wind fields from ECMWF analyses within the storm domain and to buoy wind data on a point-by-point basis. Comparison with ECMWF analyses shows that the composite winds are slightly higher and contain more mesoscale variability. Comparison with buoy d...

Planetary boundary layer and surface layer sensitivity to land surface parameters

The sensitivity of the development of the convective planetary boundary layer (PBL) and the surface layer are examined using a coupled surface parameterization and detailed PBL model. First, the coupling is verified against observations from the First ISLSCP (‘International Satellite Land Surface Climatology Project’) Field Experiment (FIFE). Results of the sensitivity experiments indicate that the PBL is most sensitive to the amount of soil water content, and the proximity of the soil water content to critical soil texture values (field capacity and wilting point). While vegetation cover is not the most sensitive parameter at the surface, its influence on the surface energy and hydrologic balance is crucial. Model sensitivity to minimum stomatal resistance, type of soil parameterization and canopy height (surface roughness and displacement depth) is also discussed.

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.